Q: SGT for GARCH estimation

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Q: SGT for GARCH estimation

enjo faes
Dear all,

In line of research conducted by 2 colleagues and me for our thesis this year, we want to examine “the importance higher moments: skewness and kurtosis of returns for VaR and cVaR estimation using GARCH for European Blue chips”.

First of all, we would like to thank Alexios Ghalanos for the package Rugarch, which is quite impressive and nice to use and Kris Boudt for explaining it on Datacamp. Some things we would like to examine further, that is: the method of implementing SGT density distribution for GARCH models. I know that there is the r package SGT. But the practical way of implementing it in R with GARCH models, does not seem clear to us at this point in time.

We look forward hearing from you. This is the first time I used the R-SIG-Finance list, so any comments are welcome for improvement.

Best regards,
Enjo Faes



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Re: Q: SGT for GARCH estimation

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Enjo,

I'm more than willing to be corrected on these matters, but if I were
you, I would immediately see moving forward in one of three ways: two of
which are technically easy but not what you want per se, and the other
is conceptually easy but is exactly what you want.

The technically easy thing to do would be to use the generalized
hyperbolic skew t student distribution or the skewed generalized error
distribution, both of which may capture the dynamics you are interested
in. The Skewed generalized error distribution is the limiting case of
the skewed generalized t distribution.

The alternative, which will give you exactly the amount of fine grained
control you want but will take a bit more work, is to implement the
maximum likelihood estimation yourself. What this (usually) means is
that you have a parameter vector β (this would include the parameters of
your mean equation, the parameters of your volatility equation, and all
of the parameters of the conditional distribution) that when given that
vector, we know what standardized residuals that implies. We can then
"score" the standardized residuals based on how they compare to what we
have assumed the conditional distribution is, and pick the highest
score. The canonical way of doing this is to take the (negative) log
transformation of the likelihood and then maximize (minimize) it as a
function of that parameter vector. Presumably the SGT package could be
helpful with this somehow.

The above approach is something of a pain but it's a good way to get
into the code yourself, and I did it for an undergraduate thesis myself
a few years ago when I implemented a non-supported GARCH model. However,
I note that this is not the point of your paper, so you may be unwilling
to do that.

Anyone else should feel free to chime in if I've said anything wrong,
missed anything in the rugarch documentation, or have generally made a
fool of myself.

Best,

Alex

On 5/2/21 2:07 AM, enjo faes wrote:

> Dear all,
>
> In line of research conducted by 2 colleagues and me for our thesis this year, we want to examine “the importance higher moments: skewness and kurtosis of returns for VaR and cVaR estimation using GARCH for European Blue chips”.
>
> First of all, we would like to thank Alexios Ghalanos for the package Rugarch, which is quite impressive and nice to use and Kris Boudt for explaining it on Datacamp. Some things we would like to examine further, that is: the method of implementing SGT density distribution for GARCH models. I know that there is the r package SGT. But the practical way of implementing it in R with GARCH models, does not seem clear to us at this point in time.
>
> We look forward hearing from you. This is the first time I used the R-SIG-Finance list, so any comments are welcome for improvement.
>
> Best regards,
> Enjo Faes
>
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> [hidden email] mailing list
> https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-finance__;!!Mih3wA!WQm5dwurdkf-eQaSUtzwNNyLuKllO-brkvG6MVTev9AC0YJgXn87Iz-tduCvr4V-$
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.

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